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KEAM 2013 Math Paper
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© examsnet.com
Question : 92
Total: 120
If
y
=
t
a
n
−
1
(
2
x
−
1
1
+
x
−
x
2
)
,
then
d
y
d
x
at
x
=
1
is equal to
1
2
2
y
1
−
1
2
3
2
Validate
Solution:
Given,
y
=
tan
−
1
(
2
x
−
1
1
+
x
−
x
2
)
=
tan
−
1
{
x
−
(
1
−
x
)
1
+
x
(
1
−
x
)
}
⇒
y
=
tan
−
1
x
−
tan
−
1
(
1
−
x
)
On differentiating w.r.t.
x
, we get
d
y
d
x
=
1
1
+
x
2
−
1
1
+
(
1
−
x
)
2
(
−
1
)
=
1
1
+
x
2
+
1
1
+
(
1
−
x
)
2
At
x
=
1
,
[
d
y
d
x
]
x
=
1
=
1
1
+
1
+
1
1
+
0
=
1
2
+
1
=
3
2
© examsnet.com
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